X-ray tomograph

ABSTRACT

A tomograph which determines projection data phase range capable of back projection for each reconfigured voxel with an arbitrary value larger than π so that the absolute values of cone angles at the ends of this phase range is minimized, calculates an approximate straight line for a curve indicating the position of a radiation source with respect to the channel direction position of parallel beam projection data obtained by a parallel beam of a parallel shape viewed from the go-around axis direction generated from the radiation source, and based on the determined projection data range capable of back projection, three-dimension back projects the parallel beam projection data subjected to filter processing created through a filter correction to the back projection region corresponding to the region in concern along the approximate irradiation trace of the radiation beam calculated using the calculated approximate straight line, thereby suppressing generation of the distortion attributed to data discontinuity, simplifying an arcsin calculation and significantly increasing the processing speed of the tomograph.

TECHNICAL FIELD

The present invention relates to a tomograph which generates atomographic image of an examinee using projection data obtained from aradiation source moving in the body axis direction relative to theexaminee through a radiation detector.

BACKGROUND ART

A conventional three-dimensional back projection method will beexplained. A Feldkamp method, Wang method, IHCB method and PI-methodproposed as three-dimensional back projection methods arethree-dimensional back projection methods which capture a cone beamspreading (having an angle of inclination) in both the slice (body axis)direction and channel (rotation) direction irradiated to multi-rowradiation detectors as a collection of a plurality of rows of fan beamsspreading only in the channel direction, carry out filter correctionprocessing similar to a two-dimensional back projection method on thefan beam projection data obtained from each detector row or parallelbeam projection data obtained by replacing the fan beam by parallel beamthrough rearrangement processing and carry out back projectionprocessing along the trace of the beam to thereby obtain a reconfiguredimage.

FIG. 7 shows a reconfigurable condition of a Wang method and FIG. 8shows a reconfigurable condition of a PI-method. Here, referencecharacter FOV denotes an effective field of view region, SOD denotes adistance between an X-ray tube and the go-around axis of a CT device andSID denotes a distance between the X-ray tube and detector. The Wangmethod is a method corresponding to a Feldkamp method adapted to imagetaking of a spiral orbit and has a back projection phase width of π to2π.

An example of a PI-method is disclosed in JP-A-11-253434. This is also aback projection method applicable to image taking of a spiral orbit andis a reconfiguration method for back projecting a π range in which thephase varies from one voxel to another to improve a bed moving speedusing the Wang method. The PI-method can set the back projection phaserange for each voxel to π by limiting the vertical direction of an X-raybeam to be back projected using a spiral located opposite to the X-rayfocal position.

An example of the IHCB method is disclosed in JP-A-11-4823. This methodconsists of an algorithm for back projecting a back projection phaserange which varies from one voxel to another and the back projectionphase width is either π or an entire possible data range which variesfrom one voxel to another.

Next, problems of these conventional technologies will be explained.

The Feldkamp method is an image reconfiguration method for image takingof a circular orbit and is not applicable to image taking of a spiralorbit. The Wang method is an image reconfiguration method for imagetaking of a spiral orbit and can correct influences of movement of anexaminee, which is practiced by the conventional two-dimensional backprojection method by extending the back projection phase width beyond π(increasing data redundancy), but results in a poor data utilizationrate and the pitch (hereinafter referred to as “measuring throughput”)of the spiral during image taking needs to be very small. By improvingthe PI-method and IHCB method so that the back projection phase rangeaccording to the Wang method is widened, their respective measuringthroughputs can be drastically improved compared to the Wang method, butthey are the back projection methods within the π range with dataredundancy completely eliminated, and therefore data may bediscontinuous at the start phase and end phase of the back projectionphase range due to influences of movement of the examinee, which islikely to become a strong artifact and appear on the image.

Here, data redundancy will be explained. The data redundancy refers to abreadth of a phase range within which not only phase data but alsoopposed phase data is acquired. According to a three-dimensional backprojection method, data redundancy changes from one voxel to another.For example, as shown in FIG. 22, when back projection is performed fromdata obtained by rotating the phase of a radiation source by 180degrees, the contributing data phase range changes from onereconfiguration pixel to another and a pixel a has data having a phaserange of 180 degrees or more, while a pixel b can only acquire data of180 degrees or less. Furthermore, it is also necessary to consider thebeam width in the body axis direction and in this way data redundancychanges from one pixel to another in a complicated manner. For thisreason, a complicated redundancy correction is required.

One of problems of these conventional three-dimensional reconfigurationsis an increase in a calculation time.

Therefore, when an increase in the amount of calculation from a parallelbeam two-dimensional back projection method to a parallel beamthree-dimensional back projection method is analyzed, the increasedcalculation causes (1) an increase in the number of timesone-dimensional rearrangement processing is performed, (2) an increasein the number of times reconfiguration filter processing is performedand (3) an addition of calculation of detector row addresses during backprojection processing. Here, the main processing that occupies thecalculation time in the two-dimensional back projection method andthree-dimensional back projection method is back projection processing.

The loads of calculation of the distance between the focus andreconfiguration point during the calculation of detector row addressesand arcsin calculation (calculation of the z position of the focus ofthe parallel beam of the following Expression 1) are particularly largeand occupy the major portion of causes of increases in the calculationtime.z _(S)=(J·(φ+arcsin(t _(I) /SOD))/2π)+z _(SO)  [Expression 1]

See FIG. 29.

Suppose SOD is a distance between a radiation source and a go-aroundaxis, φ is a phase angle of the parallel beam, J is a relative movementdistance from a radiation source to an examinee per rotation of ascanner on a radiation detector 13, t_(I) is the position in the channeldirection, z_(s) is the position of the radiation source 11 in the zdirection and z_(s0) is z_(s) when the go-around phase of the radiationsource is 0. Therefore, if these calculations can be simplified, it ispossible to significantly increase the processing speed of thetomograph.

It is an object of the present invention to provide a tomograph capableof suppressing generation of the distortion attributed to datadiscontinuity and obtaining a tomographic image of high image qualitynot eliminating data redundancy but rather using it in three-dimensionalback projection calculations.

It is another object of the present invention to provide a tomographcapable of simplifying arcsin calculation on a fan-parallel beamconversion and back projection processing according to a set FOV rangein three-dimensional back projection calculations and significantlyincreasing the processing speed of the tomograph without degrading imagequality.

DISCLOSURE OF THE INVENTION

1. In order to attain the above described objects, the present inventionis a tomograph comprising a radiation source and a radiation detectorarranged opposite to each other, between which a bed with an examineeplaced thereon is provided, the radiation source and radiation detectorturning around the bed which can be moved with respect to this go-aroundaxis, radiation irradiated from the radiation source and passing throughthe examinee being detected using the radiation detector, andreconfiguration means for creating a three-dimensional tomographic imagein a region in concern of an object from the detected projection data,wherein the reconfiguration means determines for each voxel a projectiondata range capable of back projection having an operating projectiondata phase width of 180 degrees or more, superimposes a reconfigurationfilter, assigns weights to data of the same phase or opposite phase foreach phase for this projection data range and performs three-dimensionalback projection on this filter-processed projection data over thedetermined data range capable of back projection along the irradiationtrace of the radiation beam.

Since the tomograph of the present invention determines the projectiondata phase range used for each voxel, it is possible to determine theprojection data phase range for each voxel so that absolute values ofthe angles of inclination of radiation beams become the same at bothends of the projection data, thereby use projection data with a smallcone angle, provide redundancy using weighting means and correct thedata for each voxel using a weighting function, thereby suppressinggeneration of the distortion attributed to discontinuity in the dataphase direction and obtain images of high quality. The tomograph of thepresent invention requires no redundancy processing which would requirecomplicated calculations, thus making it possible to create images athigh speed.

2. The present invention described in the item 1 is characterized inthat when determining the above described data range, a projection datarange is determined so that the difference in the absolute values ofcone angles at both ends of the projection data range used is reduced.

3. The present invention described in the item 2 is characterized inthat the projection data phase width used is determined so as to be thesame phase width for each voxel.

The tomograph according to the invention described in the items 2 and 3is characterized in that determining means for determining theprojection data phase range used for each voxel determines theprojection data range so that the difference in the absolute value ofcone angles at both ends of the actually used projection data rangebecomes small or determines the projection data range so that theprojection data phase width used has the same phase width for eachvoxel, which allows projection data with a small cone angle to be used.Furthermore, by equalizing the absolute values of angles of inclinationof radiation beams at both ends of the projection data exactly, it ispossible to calculate the position of the detector row direction fromthe data start direction or end direction simultaneously and furthercalculate the same phase range at the time of back projection of eachreconfigured voxel and thereby determine a weighting function forredundancy corrections using a single expression and performcalculations at high speed.

4. The present invention described in the item 1 is characterized inthat the projection data range capable of back projection is either 270degrees or 360 degrees.

The tomograph of the present invention described in the item 3 useseither 270 degrees or 360 degrees as the projection data range capableof back projection, and assigns weights to data using 270 degrees in thephase direction, and can thereby reduce discontinuity at the data end toa minimum. This 270-degree data corrects a discontinuity at the180-degree data end using a data phase with smallest discontinuityhaving a 90-degree phase difference and can reduce data discontinuity toa minimum, and thereby realize reconfiguration of high quality.

5. The invention described in any one of the items 1 to 4 ischaracterized in that projection data whose number of images taken perrotation is a multiple of the number of sides C of a polygonal displaypixel is acquired and the reconfiguration means comprises backprojection means for superimposing the reconfiguration filter on thisprojection data, grouping data at the same channel position and havingprojection phases in the go-around direction shifting by Nπ/2 (N=1, 2,3, . . . ) [rad] at a time and performing back projection to a squareimage array group by group.

6. The invention described in any one of the items 1 to 4 ischaracterized in that the reconfiguration means converts the projectiondata obtained to data including fan beam data and parallel beam datawhose number of images taken per rotation is a multiple of the number ofsides C of a polygonal display pixel, superimposes the filter on thisprojection data, groups data at the same channel position and havingprojection phases in the go-around direction shifting by Nπ/2 (N=1, 2,3, . . . ) [rad] at a time and performs back projection to a squareimage array group by group.

The tomograph of the invention described in the items 5 and 6 is amethod for enhancing the speed of back projection requiring the maximumcalculation time in creating an image. In order to enhance the speed ofback projection, the present invention takes advantage that the shape ofthe reconfigured image array is polygonal and that image taking isperformed while circling around the reconfigured image, the inventiondescribed in the item 5 takes images with a view which is a multiple ofthe number of sides of a display pixel, performs fan beamreconfiguration and the invention described in the item 6 converts datato data whose number of views is a multiple of the number of sides of adisplay pixel through rearrangement processing and performs parallelbeam reconfiguration. In all cases, the invention groups projection datawhose phase in the go-around direction shifts by Nπ/2 (N=1, 2, 3, . . .) [rad] at a time, back projects the square image group by group, andcan thereby reduce the number of times the channel direction position ina full reconfiguration and interpolation coefficient are calculated.This is because when the reconfigured image is square, the data of aphase differing exactly by Nπ/2 (N=1, 2, 3, . . . ) [rad] and the squarereconfigured image have the same positional relationship. Furthermore,the number of views is set to a multiple of 4 to calculate data of aphase differing by Nπ/2 (N=1, 2, 3, . . . )[rad] exactly and it ispossible to create images by calculating channel positions within arange of ¼ of a full revolution (π/2 [rad]) in the cases of both a fullreconfiguration and a half reconfiguration. In this way, in the case ofa full reconfiguration, the amount of calculation becomes ¼ and thoughcalculations are carried out using one calculator, a calculation resultclose to a result of a parallel calculation using four calculators canbe obtained and it is possible to realize high performance at low cost.

7. The invention described in any one of the items 1 to 6 ischaracterized in that associating means is provided for associatingpixel intervals in the body axis direction of the image using polygonaldisplay pixels with the relative moving speed between the object and theradiation source in the go-around axis direction.

8. Furthermore, the invention described in the item 7 is characterizedin that the associating means is constructed so that the relationshipbetween pixel interval rpitch in the body axis direction of the squareimage and the relative moving speed J in the go-around axis direction ofthe object and the radiation source is expressed by J=2·N·rpitch (N=1,2, 3 . . . ).

9. The tomograph according to the invention described in the items 7 and8 is characterized in that at the phase of Nπ (N=1, 2, 3 . . . ) [rad]of the radiation source, the position on the radiation detector at whichthe beam passing through a voxel I (x, y, z) whose body axis directionposition is Z [mm] and a voxel I (−x, −y, NJ/2+Z) whose body axisdirection position is N·J/2+Z[mm] intersects remains the same, andtherefore when a beam passing through a voxel is calculated at a certainview at the time of back projecting, this is equivalent to simultaneouscalculations of the row positions of phases differing by Nπ (N=1, 2, 3,. . . ) [rad] from each other and when an image is generated from datawith a plurality of revolutions obtained by taking images through spiralscanning, it is possible to enhance the speed of back projection whichrequires a maximum time for image generation.

10. Furthermore, the present invention is a tomograph comprising aradiation source and a radiation detector made up of two-dimensionallyarranged detection elements, arranged opposite to each other, betweenwhich a bed with an examinee placed thereon is provided, the radiationsource and radiation detector turning around the bed which can be movedwith respect to this go-around axis, radiation irradiated from theradiation source and passing through the examinee being detected usingthe radiation detector, and reconfiguration means for creating athree-dimensional tomographic image in a region in concern of theexaminee from the detected projection data, wherein the reconfigurationmeans determines a projection data phase range capable of backprojection for each reconfigured voxel, calculates an approximatestraight line for a curve indicating the radiation source position withrespect to the channel direction position of parallel beam projectiondata corresponding to the region in concern obtained by a parallel beamof a parallel shape viewed from the go-around axis direction generatedfrom the radiation source, corrects each row of the projection data bymultiplying a coefficient which is dependent on the angle of inclinationof radiation from the radiation source, carries out one-dimensionalrearrangement processing for obtaining parallel beam projection datafrom the fan beam projection data obtained from a fan-shaped fan beamviewed from the go-around axis direction generated from the radiationsource, and superimposes the reconfiguration filter on the parallelprojection data to generate filter-processed parallel projection dataand three-dimension back projects the parallel beam projection datasubjected to the filter processing based on the determined projectiondata range capable of back projection to the back projection regioncorresponding to the region in concern along the approximate irradiationtrace using the approximate straight line.

The tomograph of the present invention three-dimension back projects thefilter-processed parallel beam projection data to the back projectionregion corresponding to the region in concern based on the projectiondata range capable of back projection determined by the operating dataphase range calculating means along the approximate irradiation trace ofthe radiation beam calculated using an approximate straight line by theapproximate straight line calculating means for calculating anapproximate straight line for the curve indicating the radiation sourceposition relative to the channel direction position corresponding to theregion in concern of the parallel beam projection data obtained by theparallel beam of a parallel shape viewed from the go-around axisdirection generated from the radiation source, and therefore as opposedto the conventional focus position calculation of a parallel beam whichincludes arcsin calculation and has an increased load, this arcsincalculation is replaced by an approximate straight line, simplifying theamount of calculation in the parallel beam three-dimensional backprojection method and thereby significantly increasing the processingspeed of the tomograph.

11. The present invention described in the item 10 is characterized inthat the reconfiguration means performs redundancy correction weightingfor generating a weighting factor from a weighting function in the phasedirection to correct data redundancy at each phase according to thephase width of this determined projection data, and the parallel beamthree-dimensional back projection means assigns the weighting factorobtained by the redundancy correction weighting means to the projectiondata within the determined projection data phase range and performsthree-dimensional back projection along the approximate trace to theback projection region.

12. The tomograph of the present invention described in the item 11 ischaracterized in that in determining the projection data phase range, itis possible to determine the phase range of fπ [rad] in the viewdirection and perform a redundancy correction using the weightingfunction by the redundancy correction weighting means. Thus, it ispossible to provide data with redundancy (extending the back projectionphase width beyond 180 degrees), assign weights using the weightingfunction, reduce discontinuity at the data ends (at the start/end ofimage taking) and obtain an image with the influence of movement of theexaminee reduced to a minimum.

13. Furthermore, the invention described in the item 10 is characterizedin that the operating data phase range calculation means determines theprojection data range capable of back projection for each reconfiguredvoxel so that the maximum cone angle of the beam back projected for eachvoxel becomes narrowest.

The tomograph of the invention described in the item 13 determines theback projection phase range for each voxel by the operating data phaserange calculation means so that the maximum cone angle becomes aminimum, and can thereby reduce influences of deterioration of imagequality by the cone angle to obtain better image quality and improve therelative moving speed (so-called measuring throughput) between theexaminee and focus in the Z direction.

14. Furthermore, the invention described in the item 10 is characterizedin that in calculating the operating data phase range calculation, theprojection data range capable of back projection for each reconfiguredvoxel is determined so that the phase direction range of the beam backprojected for each voxel is set to the narrowest possible range.

The tomograph of the invention described in the item 14 determines theback projection phase range for each voxel by the operating data phaserange calculation means so that the number of views becomes small, andcan thereby improve time resolution for each voxel. Furthermore,combining the invention with the redundancy correction weighting meansdescribed in the item 13 can obtain better image quality in a regionwhere the examinee moves fast. Furthermore, by setting the backprojection phase range for each voxel to the time range in which imagesare taken at the same time whenever possible so that the time positionof the respective voxels in the displayed images come closer to oneanother, it is possible to shorten the time width contributing to thereconfigured image and improve time resolution.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic view of a tomograph of the present invention;

FIG. 2 is a block diagram of the tomograph shown in FIG. 1;

FIGS. 3A and 3B are conceptual diagrams showing a focus trace of acircular orbit scan and spiral orbit scan;

FIGS. 4A and 4B are side views of the waist part of a single radiationdetector and multi-row radiation detector;

FIGS. 5A and 5B illustrate a collimation thickness of an X-ray beam perrow of the single radiation detector and multi-row radiation detector;

FIG. 6 is a flow chart showing a processing operation by generalreconfiguration means;

FIG. 7 is a plan view showing a positional relationship between theradiation detector 13 and beam as a reconfigurable condition accordingto a Wang method;

FIG. 8 is a plan view showing a positional relationship between theradiation detector 13 and beam as a reconfigurable condition accordingto a PI-method;

FIG. 9 is a flow chart showing a processing operation of an embodimentof the reconfiguration means of the present invention;

FIG. 10 is a flow chart showing an operation of the operating dataposition range determining processing shown in FIG. 9;

FIGS. 11A and 11B are a perspective view and an exploded view showingspiral traces of the radiation source and radiation detector;

FIGS. 12A and 12B are a perspective view and an exploded viewillustrating the operation of the rearrangement processing shown in FIG.9;

FIGS. 13A and 13B are a perspective view and an exploded viewillustrating other rearrangement processing;

FIG. 14A is a spiral measuring diagram when 180-degree data is used;

FIG. 14B is a characteristic diagram showing a weighting functioncorresponding to spiral measurement when 180-degree data is used;

FIG. 15A is a spiral measuring diagram when 270-degree data is used;

FIG. 15B is a characteristic diagram showing a weighting functioncorresponding to other spiral measurement when 270-degree data is used;

FIG. 16 is a flow chart showing a processing operation of anotherembodiment of the reconfiguration means of the present invention;

FIG. 17 is a perspective view showing an example of a back projectiondata phase range when 180-degree phase range (f=1) is used;

FIG. 18 is a perspective view showing an example of a back projectiondata phase range when a phase range (1<f<2) from 180 degrees to 360degrees is used;

FIG. 19 is a perspective view showing an example of back projection dataphase range when 360-degree phase range (f=2) is used;

FIGS. 20A and 20B are characteristic diagrams of a weighting functionillustrating the redundancy weighting processing shown in FIG. 16;

FIGS. 21A to 21C are characteristic diagrams of a weighting function foreach phase illustrating redundancy weighting processing shown in FIG.16;

FIG. 22 is a plan view showing a phase range capable of back projection;

FIG. 23 is a flow chart showing a processing operation of anotherembodiment of the reconfiguration means of the present invention;

FIG. 24 is a flow chart showing a processing operation of anotherembodiment of the reconfiguration means of the present invention;

FIG. 25 illustrates back projection in group units in the groupingprocessing shown in FIG. 23;

FIG. 26 illustrates another back projection in group units in thegrouping processing shown in FIG. 23;

FIG. 27 is a flow chart showing a processing operation of a furtherembodiment of the reconfiguration means of the present invention;

FIGS. 28A, 28B and 28C show a relationship between the figureillustrating calculation processing of the approximate straight lineshown in FIG. 27, cone angle, X-ray source and reconfiguration;

FIG. 29 illustrates determining processing of the projection data phaserange;

FIG. 30 is a flow chart showing a processing operation of a stillfurther embodiment of the reconfiguration means of the presentinvention;

FIG. 31 is a flow chart showing an operation of phase range calculationprocessing on the data used in FIG. 30; and

FIG. 32A to FIG. 32D show a relationship between a fan beam and parallelbeam.

BEST MODE FOR CARRYING OUT THE INVENTION Embodiment 1

With reference now to the attached drawings, embodiments of the presentinvention will be explained in detail below.

FIG. 1 is a schematic outside view of a tomograph according to anembodiment of the present invention. The tomograph comprises a scanner 1used for image taking, a bed 2 to place and move an examinee, an inputdevice 3 made up of a mouse and keyboard, etc., for inputting measuringreconfiguration parameters such as bed moving speed information andreconfiguration position, a calculation device 4 for processing dataobtained from a multi-row detector and a display device 5 which displaysa reconfigured image.

FIG. 2 is a block diagram of the tomograph shown in FIG. 1.

The scanner 1 consists of a bed 2, a high voltage switching unit 8, ahigh voltage generation device 9, a radiation source 11 such as aradiation generation device having a radiation control device 10, aradiation detector 13 placed opposite to the radiation source 11 withrespect to an examinee 12, a go-around drive device 14 which drives thisradiation detector 13 and radiation source 11 in the go-around directionand a collimator 15 which controls a radiation region to be irradiatedfrom the radiation source 11, etc. The scanner 1 further consists of acollimator control device 16 which controls the collimator 15, a scannercontrol device 17 which controls the go-around drive device 14, a bedmovement measuring device 19 which measures an amount of relativemovement between the bed control device 18 which controls the bed 2 anda central control device 20 which controls these devices.

Image taking conditions (bed moving speed, tube current, tube voltage,slice position, etc.) and reconfiguration parameters (region in concern,reconfigured image size, back projection phase width, reconfigurationfilter function, etc.) are input from the input device 3, a controlsignal necessary for image taking is sent from the central controldevice 20 to the radiation control device 10, bed control device 18 andscanner control device 17 based on the instruction and upon reception ofan image taking start signal, image taking is started. When image takingis started, the radiation control device 10 sends a control signal tothe high voltage generation device 9, a high voltage is applied to theradiation source 11, and radiation is irradiated from this radiationsource 11 to the object 12. At the same time, a control signal is sentfrom the scanner control device 17 to the go-around drive device 14, andthe radiation source 11, radiation detector 13 and preamplifier 21 turnrelative to the object 12. On the other hand, the bed 2 carrying theexaminee 12 is stopped by the bed control device 18 during a circularorbit scan or translated in parallel in the go-around axis direction ofthe radiation source 11, etc., during a spiral orbit scan. The go-arounddrive device 14, scanner control device 17 and bed control device 18,etc., constitute a drive device which turn the radiation source 11 andradiation detector 13 relative to the examinee 12 and which isrelatively movable in the axial direction of the examinee 12.

With the irradiation region restricted by the collimator 15, theradiation irradiated from the radiation source 11 is absorbed andattenuated by each tissue inside the examinee 12, passed through theexaminee 12 and detected by the radiation detector 13. The radiationdetected by the radiation detector 13 is converted to a current,amplified by the preamplifier 21 and input to the calculation device 4as a projection data signal. The projection data signal input to thecalculation device 4 is processed by the reconfiguration means 22 forreconfiguring the image inside the calculation device 4.

The reconfigured image is saved in a storage device 23 in an I/O device50 and displayed by an image processing device 26 on the display device5 as a tomographic image.

FIGS. 3A and 3B are conceptual diagrams showing focus orbits of acircular orbit scan and spiral orbit scan.

FIG. 3A shows a movement trace 24 a of the radiation source (focus)during a circular orbit scan and FIG. 3B shows a movement trace 24 b ofthe radiation source (focus) during a spiral orbit scan. If the detectoris formed of a single row, when images are taken on a circular orbit asin the case of the movement trace 24 a it is possible to accuratelyreproduce the images at the positions of the radiation source bycarrying out filter correction two-dimensional back projection. However,when images are taken on a spiral orbit as in the case of the movementtrace 24 b, carrying out filter correction two-dimensional backprojection alone results in streak-shaped artifact at that position dueto data discontinuity at the end position of image taking. Thus, byapplying data interpolation to the data obtained on the spiral orbit asin the case of the movement trace 24 b, the data is corrected to thecircular orbit data like the movement trace 24 a and then filtercorrection two-dimensional back projection is carried out. In this way,it is possible to obtain an image with reduced discontinuity. The degreeof artifact in this case is determined by the degree of discontinuity inthe X-ray source trace, that is, the degree of artifact changesdepending on the moving speed of the examinee. For example, in a singlerow type spiral scanning X-ray tomograph (SDCT), the spiral pitch (ratioof the moving speed of the examinee to the thickness of the X-ray beamin the go-around axis direction) is generally used to an extent thatsubstantially the entire image taking region can be covered with thedata on the opposite side taken into consideration.

FIGS. 4A and 4B are schematic side views of the single row radiationdetector 13 a and multi-row radiation detector 13 b.

In FIG. 4B, a plurality of multi-row radiation detectors 13 b whosewidth per row is narrower than that of the single row radiation detector13 a in FIG. 4A are arranged in a plurality of rows in the go-aroundaxis direction, realizing a wider detector than the single row radiationdetector 13 a as a whole.

FIGS. 5A and 5B are schematic side views illustrating a thickness in thego-around axis direction (hereinafter, referred to as a “detectorcollimation thickness DCT”) of the radiation beam per one row ofdetectors at the position of the collimator 15 in the case of using thesingle row radiation detector 13 a and the multi-row radiation detector13 b, respectively.

In the case of the multi-row radiation detector 13 b shown in FIG. 5B,the detector collimation thickness DCT is smaller than that of thesingle row radiation detector 13 a shown in FIG. 5A, but images over awider range can be taken at a time as a whole. The spatial resolution(body axis resolution) in the go-around axis direction of thetomographic image obtained improves as the detector collimationthickness becomes smaller.

Next, the processing of creating a three-dimensional tomographic imageof the object 12 by the reconfiguration means 22 from the projectiondata detected by the radiation source detector 13 will be explained.

FIG. 6 is an example of flow chart showing the processing according tothe Feldkamp reconfiguration method.

On the other hand, FIG. 9 is a flow chart showing a processing operationof the reconfiguration means 22 of the tomograph according to anembodiment of the present invention. This flow chart assumes processingcarried out slice by slice.

The reconfiguration means 22 in FIG. 2 is provided with operating dataphase range calculation means for determining a projection data phaserange capable of back projecting for each reconfigured voxel, cone anglecorrection means for multiplying each row of projection data by acoefficient which is dependent on the angle of inclination of radiationfrom the radiation source, one-dimensional rearrangement processingmeans for obtaining parallel beam projection data from fan beamprojection data obtained from a fan-shaped fan beam viewed from thego-around axis direction generated from the radiation source, filtercorrection means for superimposing the reconfiguration filter on theparallel beam projection data and creating filter-processed parallelbeam projection data and parallel beam three-dimensional back projectionmeans for carrying out three-dimensional back projection on thefilter-processed parallel beam projection data to the back projectionregion corresponding to a region in concern based on the determinedprojection data range capable of back projection.

Based on the above described configuration, in FIG. 9, the operatingdata phase range calculation means determines the data range used foreach voxel in step S4 first. Next, in step S5, the cone angle correctionmeans multiplies each row of the projection data by a coefficient whichis dependent on the angle of inclination of radiation and in step S6,the one-dimensional rearrangement processing means associates the fanbeam projection data obtained from a fan-shaped fan beam viewed in thego-around axis direction generated from the radiation source with theparallel beam projection data. Then, in step S7, the filter correctionmeans superimposes the reconfiguration filter on the parallel beamprojection data and generates filter-processed parallel beam projectiondata. Next, in step S8, the parallel beam three-dimensional backprojection means performs three-dimensional back projection on thefilter-processed parallel beam projection data to the back projectionregion corresponding to the region in concern based on the determinedprojection data range capable of back projection.

Next, the respective steps shown in FIG. 9 will be explained.

First, in step S4, the operating data phase range calculation meansdetermines each data range used for each of all voxels in the slice.

In the geometry shown in FIGS. 28A, 28B and FIG. 29, suppose thedistance between the radiation source 11 and rotation center is SOD, therelative movement distance in the body axis direction of the radiationsource 11 with respect to the examinee per rotation of the scanner onthe radiation detector 13 (e.g., amount of feeding of the table) is J,the go-around phase of the fan beam source is β, beam spreading anglebetween the beam directed to the reconfigured voxel I (x, y, z) andcentral beam is α and the go-around phase of the parallel beam is φ.Then, the fan beam source position S(β)=S(x_(S), y_(S), z_(S)) isexpressed by the following Expression 2. Furthermore, when this isrearranged and replaced by a parallel beam, the fan beam source positionis expressed by Expression 3.S(β)=S(SOD·sin β,−SOD·cos β,Jβ/2π)  [Expression 2]S(φ)=S(SOD·sin(φ+α),−SOD·cos(φ+α),J(φ+α)/2π)  [Expression 3]

Here, suppose the traveling direction of the parallel beam is W, thedirection perpendicular to this traveling direction W (channel directionof parallel beam) is T. Then, the T coordinate and W coordinate when theparallel beam at phase φ passes through coordinate (x, y) are expressedby Expression 4 and Expression 5 respectively.T(x,y,φ)=x·cos φ+y·sin φ  [Expression 4]W(x,y,φ)=−x·sin φ+y·cos φ  [Expression 5]

Furthermore, the distance s_tz_dist between the X-ray source and T-Zplane (plane passing through the go-around axis and perpendicular to theparallel beam) is expressed by the following Expression 6.s _(—) tz_dist(x,y,φ)=(SOD ² −T(x,y,φ)²)^(1/2)  [Expression 6]

Furthermore, when the parallel beam with phase φ passes through thereconfigured voxel I (x, y, z) and crosses the radiation detector 13whose distance from the radiation source 11 is SID, suppose thecoordinates of a system formed of the V axis (the same go-around axisdirection as the z axis, the origin position thereof is detector center)of the radiation detector 13 and the X-Y axis are H (x, y, φ). Then, thecoordinates are expressed by Expression 7. Here, while the Z axismatches the V axis, they are different in that the Z axis uses the scanstart position as the origin position and the V axis uses the detectorcenter as the origin position.H(x,y,φ)=(z−J(φ+α)/2π)·SID/(s _(—) tz_dist(x,y,φ)+W(x,y,φ))  [Expression7]

Here, in FIG. 28A, α=arcsin(t/SOD)=A′t+B′, A′ and B′ are coefficients ofapproximate straight lines obtained by approximating arcsin(t/SOD).

Based on FIG. 28C, how the phase range calculated in step S4 isdetermined will be explained. As already described, this phase rangediffers from one voxel to another, and therefore the phase range isdetermined for each voxel and expressed by f here. The phase range isdetermined by selecting one which narrows the plane spreading angle ofthe cone beam with respect to the vertical line in the detectordirection, that is, cone angle most. f is normally between 1 and 2. AtB_(s) and B_(e) which are the ends of phase range fπ used to backproject the reconfigured voxel I (x, y, z), in order to minimize theabsolute value of the cone angle, it is possible to select a go-aroundphase φ of the parallel beam so that the difference in the absolutevalues between the coordinates H(x, y, φ+fπ) (corresponds to finallydetermined cone angle) and coordinates H(x, y, φ) (corresponds toinitial cone angle) become the smallest possible value. Morespecifically, an example of calculation algorithm of the data range withthe smallest cone angle is shown in FIG. 10. As shown in step S101, whenit is assumed that the initial value of φ is −fπ/2, calculation phaseaccuracy is Q (phase angle per view is normally used as Q, but whenpriority is given to the processing time, a phase angle exceeding oneview can also be used), the sum of the H(x, y, φ+fπ) and H(x, y, φ) iserr(x, y, φ) (hereinafter expressed as “err”) and a minimum value ofthis sum err is err_min (initial value is err_min=fπ), err is expressedby Expression 8 and Expression 9 shown in step S102.err=H(x,y,φ)+H(x,y,φ+fπ)  [Expression 8]if [err_min>err],err_min=err  [Expression 9]

Here, when φ increases, err decreases and when φ decreases, errincreases, and so the following Expression 10 and Expression 11 arerepeated.if [err>0],φ=φ+Q  [Expression 10]if [err<0],φ=φ−Q  [Expression 11]

Through this repeating processing, if err is compared with err_min asshown in step S103, when err becomes a minimum value, minimum valuesappear repeatedly and err=err_min, and so by carrying out repeatingprocessing until err=err_min is obtained, it is possible to select φ asshown in step S104 so that the difference in the absolute values betweencoordinates H(x, y, φ+fπ) and coordinates H(x, y, φ) becomes thesmallest possible value as shown in step S105. If the decision in stepS105 results in err>0, φ=φ+Q as in step S107, and if err<0, φ=φ−Q as instep S108. Thus, the phase range (Bs≦φ<Be) is expressed by the followingExpression 12 and Expression 13.Bs(x,y,z)=φ  [Expression 12]Be(x,y,z)=φ+fπ  [Expression 13]

Here, the phase range has been determined using the simplest method asdescribed above, but this is the problem of calculation of a minimumvalue of the function err (φ) in the phase range (−fπ/2≦φ<fπ/2) and itis also possible to use an existing method, for example, Brent's methodand golden division method (golden section search) and combine variousmethods to calculate φ and φ+fπ so that err(φ) becomes a minimum value.Furthermore, it is also possible to increase the processing speed byoptimizing the initial value when φ=−fπ/2 is determined.

Furthermore, with regard to the phase range fπ used to back project thereconfigured voxel (x, y, z), it is also possible to determine Bs and Beby determining go-around phase φ of the parallel beam so that theabsolute value of the angle of inclination of the beam (cone angle) ofthe X-ray beam becomes small at the end of the phase rangeπ and extendthe data range to both ends of the data range as shown the followingExpression 14 and Expression 15.Bs(x,y,z)=φ−(f−1)π/2  [Expression 14]Be(x,y,z)=φ+fπ+(f−1)π/2  [Expression 15]

Next, the cone angle correction step of multiplying each row of theparallel beam projection data by a coefficient which is dependent on thecone angle using the cone angle correction means in step S5 shown inFIG. 9 will be explained.

Filter correction in reconfiguration is filtering corresponding to thedistance from the go-around axis in the reconfigured image and it isnecessary to apply a filter corresponding to the cone angle to correctthe influences of beam inclination. Here, suppose data before filtercorrection is P_(para)(φ, t, v), data after filter correction isfP_(para)(φ, t, v), and the reconfiguration filter function is g(t).Then, the reconfiguration filter processing can be expressed as shown inExpression 16 using a convolution method and of this, the cone anglecorrection is the portion expressed by Expression 17. As is evident fromExpression 16, since the cone angle correction term is a coefficientcorresponding to the detector row position v (cone angle), cone anglecorrection can be carried out both before and after filter correction.For this cone angle correction, a publicly known technology in thethree-dimensional back projection techniques including a Feldkamp methodis applicable.

$\begin{matrix}{{{fp}_{para}\left( {\phi,t,v} \right)} = {\int_{- \infty}^{\infty}{\frac{SID}{\sqrt{{SID}^{2} + v^{2}}}{P_{para}\left( {\phi,{t - t^{\prime}},v} \right)}\;{g\left( t^{\prime} \right)}\;{\mathbb{d}t^{\prime}}}}} & \left\lbrack {{Expression}\mspace{14mu} 16} \right\rbrack\end{matrix}$where t′ is a variable of integration in Expression 16.SID/√{square root over (SID²+v²)}  [Expression 17]

Next, the rearrangement processing (rebinning) using the one-dimensionalrearrangement processing means in step S6 shown in FIG. 9 will beexplained. Here, FIG. 32A and FIG. 32B show a relationship between a fanbeam and a parallel beam. FIGS. 32A to 32C show a 180° reconfigurationof a fan beam and FIG. 32D shows a 180° reconfiguration of a parallelbeam. When X-ray beams (S1 to S3) irradiated in the same vectordirection viewed from the go-around axis direction are gatheredtogether, it is possible to virtually create a parallel beam as shown inFIG. 32D.

In order to enhance the calculation speed, one-dimensional rearrangementprocessing is carried out which rearranges a fan beam irradiated in afan shape viewed from the go-around axis direction as shown in FIG. 11Aand FIG. 11B into parallel beams which are parallel viewed from thego-around axis as shown in FIG. 12A (FIG. 12B is an exploded view ofFIG. 12A) and FIG. 12B. Furthermore, FIGS. 13A and 13B show the parallelbeams rearranged in the go-around axis direction, which will bedescribed later.

FIGS. 11B, 12B and 13B are exploded views of beams and their respectivefocuses on the detector corresponding to FIGS. 11A, 12A and 13A. If thefan beam is represented by P_(fan)(β, α, v) and parallel beam isrepresented by P_(para)(φ, t, v), the fan beam spreading angle in thego-around direction α=arcsin(t/SOD) and β=φ+α (see FIG. 28A), andtherefore the rearrangement processing can be expressed by Expression18.P _(para)(φ,t,v)=P _(fan)(φ+α,α,v)

Next, a convolutional calculation (filter correction processing) of areconfiguration filter carried out to correct blurs of projection datausing the filter correction means in step S7 shown in FIG. 9 will beexplained.

For filter correction, two types of methods; a convolution method whichcarries out a convolutional calculation in a real space and a Fouriermethod which carries out a multiplication in a Fourier space. Theconvolution method in the former is convolutional processing on a filterfunction which has been inverse Fourier transformed in a real space. TheFourier method in the latter is processing consisting of transforminginto a Fourier space using a Fourier transform, multiplying it by afilter function (spatial frequency filter) and then applying an inverseFourier transform.

Both are processes mathematically equivalent, but filter processing in aFourier space which provides high-speed calculation is generally used.For the filter used for reconfiguration, it is possible to select anduse Shepp and Logan, Ramachandran and Lakshminarayanan or these filterfunctions which have been modified through clinical experiences based onclinical experiences. Suppose the parallel projection data isP_(para)(φ, t, v), the parallel projection data after filter processingis fP_(para)(φ, t, v) and the reconfiguration filter is G(ω). Then,Fourier space filtering according to a Fourier method can be expressedby Expression 19.

$\begin{matrix}{{{fP}_{para}\left( {\phi,t,v} \right)} = {\frac{1}{4\;\pi}{\int_{- \infty}^{\infty}{\int_{- \infty}^{\infty}{{\left( {\phi,t,v} \right) \cdot {\exp\left( {{- {\mathbb{i}}}\;\omega\; t} \right)}}{{\mathbb{d}t} \cdot {G(\omega)} \cdot {\exp\left( {{\mathbb{i}}\;\omega\; t} \right)}}\;{\mathbb{d}\omega}}}}}} & \left\lbrack {{Expression}\mspace{14mu} 19} \right\rbrack\end{matrix}$

On the other hand, when an inverse Fourier transform g(t) of G(ω) isexpressed as shown in Expression 20, the real space filtering accordingto the convolution method can be expressed by Expression 21.

$\begin{matrix}{{g(t)} = {\frac{1}{2\;\pi}{\int_{- \infty}^{\infty}{{{G(\omega)} \cdot {\exp\left( {{\mathbb{i}}\;\omega\; t} \right)}}\;{\mathbb{d}\omega}}}}} & \left\lbrack {{Expression}\mspace{14mu} 20} \right\rbrack\end{matrix}$fP _(para)(φ,t,v)=∫_(−∞) ^(∞)(φ,t−t′,v)g(t′)dt′  [Expression 21]

where t′ is a variable of integration in Expression 21.

For simplicity, the direction in which the filter is applied is assumedto be the T direction here, but it is possible to apply the filter in ahigh-dimensional direction combining the V direction, T direction and φdirection. Furthermore, the projection data is handled as continuousdata here, but since the projection data is actually discrete data, itis necessary to use a publicly known interpolation method to calculatethe projection data in a discrete manner. This discrete calculationmethod has been practiced so far and is similar to filter correction,etc., used for weighting spiral correction reconfiguration.

Further, implementation of the three-dimensional back projectioncorresponding to the data range determined by the aforementioneddetermining means in step S8 of FIG. 9 will be explained.

As shown in FIGS. 28A and 28B, if the reconfigured voxel is I(x, y, z),the V axis direction position that matches the go-around axis on acylindrical detector centered on the radiation source 11 is v and theposition on the T axis substantially orthogonal to this V axis is t,then the reconfigured voxel I(x, y, z) is expressed by Expression 22.

$\begin{matrix}\begin{matrix}{{I\left( {x,y,z} \right)} = {\frac{1}{\pi}{\int_{{Bs}{({x,y,z})}}^{{Be}{({x,y,z})}}{{{fP}_{para}\left( {\phi,t,v} \right)}\;{\mathbb{d}\phi}}}}} \\{{{where}\mspace{14mu} t} = {{x\;\cos\;\phi} + {y\;\sin\;\phi}}} \\{v = {{\left( {z - {\frac{J}{2\;\pi}\left( {\phi + \alpha} \right)}} \right)\;\frac{SID}{{{SOD}\;\cos\;\alpha} - {x\;\sin\;\phi} + {y\;\cos\;\phi}}} + {\frac{T}{2\;\pi}\alpha}}}\end{matrix} & \left\lbrack {{Expression}\mspace{14mu} 22} \right\rbrack\end{matrix}$

This algorithm handles the projection data and reconfigured image whichshould originally be handled discretely as continuous data, andtherefore it is actually desirable to use an interpolation method suchas Lagrange interpolation and calculate discretely through interpolationin three directions of the phase direction, detector row direction anddetector channel direction. To realize a high-speed calculation at thesacrifice of accuracy, the above described v can also bev=(z−Jφ/2π)·SID/(SODcos α−x sin φ+y cos φ).

According to such a filter correction three-dimensional back projectionmethod, it is possible to obtain an image of good quality with fewererrors compared to the conventional two-dimensional reconfiguration(weighting spiral correction method). Furthermore, by performing backprojection from data with minimum errors (data with a small cone angle)for each voxel to achieve higher image quality and including determiningmeans for determining the data phase range used for each voxel torealize this, or more specifically, determining the data phase range foreach voxel so that the absolute values of the angles of inclination ofradiation beams become the same at both ends of the data in the phaserange, it is possible to use projection data with a smaller cone angleand by performing corrections using a weighting function for each voxelwhile maintaining redundancy, it is possible to obtain an image withdiscontinuity in the data phase direction reduced.

Especially, by using data 270 degrees in the phase direction andperforming weighting as shown in FIG. 20A, it is possible to reducediscontinuity at the ends of data to a minimum. With this 270-degreedata, it is possible to correct the discontinuity at 180-degree dataends as shown in FIGS. 14A and 14B using the data phase with the leastdiscontinuity with a phase difference of 90 degrees as shown in FIGS.15A and 15B. Data becomes discontinuous at the position π in FIGS. 14Aand 14B, which may cause artifact. That is, it is possible to reduce thedata discontinuity to a minimum and realize reconfiguration of higherquality. Further, if it is possible to accurately equalize absolutevalues of the angle of inclination of the radiation beam (cone angle) atboth ends of data, it is also possible to calculate the detector rowdirection position from the data start direction and end directionsimultaneously and realize a high-speed calculation. Furthermore, sincethe same phase range is used during back projection of each reconfiguredvoxel, a weighting function for redundancy correction is determined by asingle expression, which allows a high-speed calculation. Errors aremutually corrected at positions of π/2, π in FIG. 15B.

Embodiment 2

FIG. 16 is a flow chart showing a processing operation of thereconfiguration means 22 according to another embodiment of the presentinvention.

In this embodiment, a filter correction is performed in step S7 shown inFIG. 9, and then redundancy correction weighting is performed in step S9and three-dimensional back projection is performed in step S8.

In the case of this embodiment, the reconfiguration means furtherincludes redundancy correction weighting means for realizing aredundancy correction using a weighting function whose shape changesaccording to the phase width with respect to filter-processed projectiondata over a projection data range fπ determined and obtained by theoperating data phase range means.

Processes in steps S4 to S8 are the same as the procedure alreadyexplained using FIG. 9 and therefore a weighting process using theredundancy correction weighting means in step S9 will be explained here.

As shown in FIGS. 17 to 19, data of 180 degrees or more is used for eachvoxel to reconfigure an image and data correction is performed throughweighting using the weighting function as shown in FIG. 20A to correctdata redundancy. More specifically, as shown in the weighting functionW(θ) in FIGS. 21A and 21B and Expression 23 to Expression 25, weightingis performed on the phase data range which varies from one voxel toanother so that the sum of weights at the same phase and opposite phaseused for back projection remains equal at the respective phases. Here,when the data width used for each voxel is B=fπ, when B=π (when f=1),weighting becomes as shown in FIG. 21A, likewise when B=3π/2 (whenf=3/2), weighting becomes as shown in FIG. 21B and when B=2π (when f=2),weighting becomes as shown in FIG. 21C.W(θ)=((B/2)+θ)/B−π  [Expression 23]where [−π/2<θ≦(2π−B)/2].W(θ)=1  [Expression 24]where [−(2π−B)/2<θ≦(2πB)/2].W(θ)=((B/2)−θ)/B−π  [Expression 25]where [(2π−B)/2<θ≦B/2].

In FIG. 20A and FIGS. 21A to 21C, weighting which linearly changes inthe view direction is performed, but it is also possible to performweighting which changes nonlinearly in the view direction as shown inFIG. 20B. The nonlinear weighting function W′(θ) shown in FIG. 20B canbe calculated, for example, from the above described weighting functionW(θ) as shown in Expression 26 to Expression 28. Furthermore, only thecase with B≦2π is described here, but the case with B>2π can also beeasily calculated based on a similar concept.W′(θ)=3(W(θ))²−2(W(θ))³  [Expression 26]where [−π/2<θ≦(2−B)/2].W′(θ)=1  [Expression 27]where [−(2−B)/2<θ≦/(2π−B)/2].W′(θ)=−3(W(θ))²+2(W(θ))³  [Expression 28]where [(2π−B)/2<θ≦B/2].

In the above described phase range calculation process for each voxel,such a tomograph is a three-dimensional reconfiguration method whichdetermines a phase range of fπ [rad] in the view direction and carriesout a redundancy correction using a weighting function, and providesdata with redundancy (extends the back projection phase width beyond 180degrees), assigns weights using the weighting function, and can therebyreduce discontinuity at the data ends (at the start/end of image taking)and obtain an image with the influence of movement of the examineereduced to a minimum.

When a fan beam reconfiguration is used in a Wang method or IHCB methodof the conventional examples, the redundancy (projection phase range) ofprojection data obtained varies from one voxel to another. For example,when the radiation source performs back projection from data obtained byrotating the phase by 180 degrees as shown in FIG. 22, the data phaserange capable of back projection varies from one reconfiguration pixelto another and data in a phase range of 180 degrees or more is obtainedat pixel a, but only data of 180 degrees or less is obtained at pixel b.Thus, because data redundancy varies from one pixel to another, whenback projection is performed from projection data of 360 degrees orless, complicated redundancy correction processing is required at thetime of back projection. In a three-dimensional reconfiguration inparticular, a cone angle needs to be considered, and therefore morecomplicated redundancy correction processing is required, whichconstitutes one of causes of an increase in the calculation time.Furthermore, this redundancy correction processing is also associatedwith measuring throughput (relative moving speed between the focus andexaminee). Unlike these conventional examples, the present applicationrather takes advantage of redundancy, uses data with a phase range of180 degrees or more for each voxel and thereby prevents generation ofdiscontinuity due to movement, etc., and also improves the dataefficiency.

Embodiment 3

FIG. 23 is a flow chart showing a processing operation ofreconfiguration means 22 according to a further embodiment of thepresent invention.

As shown in FIG. 23, after processes in step S4 and step S5, thisembodiment carries out a rearrangement process on projection data of animage taken with a view of a multiple of 4 in step S11. Then, in stepS7, a filter correction is performed and in step S12, projection datawhose phase in the go-around direction differs by Nπ/2 (N=1, 2, 3, . . .) [rad] is grouped by grouping means and in step S9, a redundancycorrection weighting process is carried out and in step S8, the groupedprojection data is back projected to a square image group by group.

In order to realize such processing, means for acquiring projection datawhose number of images taken per rotation is a multiple of 4 isprovided, the reconfiguration means 22 includes means for superimposinga filter on this projection data, grouping means for grouping data atthe same channel position and whose projection phase in the go-arounddirection differs by Nπ/2 (N=1, 2, 3, . . . ) [rad] and back projectionmeans for back projecting into a square image array group by group usingthis grouping means.

Thus, in order to enhance the speed of back projection which takes amaximum calculation time in creating an image, an image is taken with aview of a multiple of 4 and a fan beam is reconfigured in FIG. 23, anddata is converted to data whose number of views is a multiple of 4through the rearrangement process in step S13 and a parallel beam isreconfigured in FIG. 24, taking advantage of the fact that thereconfigured image array is square and images are taken while thedetector is going around the reconfigured image.

In both cases, projection data whose phase in the go-around directiondiffers by Nπ/2 (N=1, 2, 3, . . . ) [rad] is grouped and back projectionis performed on the square image group by group, and therefore it ispossible to reduce, for example, the number of calculations of thechannel direction position in a full reconfiguration and interpolationcoefficient to ¼ (it is possible to reduce the number of calculations to½ in a half reconfiguration). This is because if the reconfigured imageis square, data whose phase differs by Nπ/2 (N=1, 2, 3, . . . ) [rad]and the square which is the reconfigured image have the same positionalrelationship.

Furthermore, the number of views is set to a multiple of 4 is toaccurately calculate data whose phase differs by Nπ/2 (N=1, 2, 3, . . .) [rad]. Furthermore, in both cases of full reconfiguration and halfreconfiguration, it is possible to create images by calculating thechannel position within a range of ¼ (π/2[rad]) of one revolution. Interms of a full reconfiguration, the amount of calculation becomes ¼ andthough the calculation is performed using only one calculator, it ispossible to obtain a result close to the case where parallelcalculations are performed using four calculators. That is, it ispossible to realize high performance at a low cost. Needless to say, itis also possible to set the number of views to a multiple of 4 duringimage taking and perform reconfiguration directly from a fan beamwithout any rearrangement process (rebinning). Furthermore, when adisplay pixel is a hexagon, it is possible to group projection datawhose phase in the go-around direction differs by Nπ/3 [rad] (N=1, 2, 3,. . . ) and back project to the hexagonal image group by group. When thedisplay pixel is polygonal and has C sides, the above described phase inthe go-around direction is 2π/C [rad].

Next, group-by-group back projection will be explained.

First, as shown in FIG. 25, when only the X-Y plane is considered and abeam passing through a voxel (x, y) irradiated from a focus positionS(β) having phase β is irradiated to a position u on the detector,group-by-group back projection processing is expressed by Expression 29to Expression 32.

FIG. 25 shows a case where the amount of calculation in the channeldirection is ¼ (view=4N; N is an integer) and the calculation startposition is not limited. Furthermore, reference numeral 131 denotes areconfiguration region.

$\begin{matrix}{{I\left( {x,y} \right)} = {\frac{1}{\pi}{\int_{{Bs}{({x,y})}}^{{{Bs}{({x,y})}} + \frac{\pi}{2}}{{{fP}_{para}\left( {\phi,t,v} \right)}\;{\mathbb{d}\phi}}}}} & \left\lbrack {{Expression}\mspace{14mu} 29} \right\rbrack \\{{I\left( {y,{- x}} \right)} = {\frac{1}{\pi}{\int_{{Bs}{({x,y})}}^{{{Bs}{({x,y})}} + \frac{\pi}{2}}{{{fP}_{para}\left( {{\phi + \frac{3\pi}{2}},t,v} \right)}\;{\mathbb{d}\phi}}}}} & \left\lbrack {{Expression}\mspace{14mu} 30} \right\rbrack \\{{I\left( {{- x},{- y}} \right)} = {\frac{1}{\pi}{\int_{{Bs}{({x,y})}}^{{{Bs}{({x,y})}} + \frac{\pi}{2}}{{{fP}_{para}\left( {{\phi + \pi},t,v} \right)}\;{\mathbb{d}\phi}}}}} & \left\lbrack {{Expression}\mspace{14mu} 31} \right\rbrack \\{{I\left( {{- y},x} \right)} = {\frac{1}{\pi}{\int_{{Bs}{({x,y})}}^{{{Bs}{({x,y})}} + \frac{\pi}{2}}{{{fP}_{para}\left( {{\phi + \frac{\pi}{2}},t,v} \right)}\;{\mathbb{d}\phi}}}}} & \left\lbrack {{Expression}\mspace{14mu} 32} \right\rbrack\end{matrix}$

A beam irradiated from phase β+π/2 and passing through a voxel (−y, x)is irradiated to the position u on the radiation detector as in the caseof being irradiated from phase β to a voxel (x, y). Likewise, a beamirradiated from phase β+π passes through a voxel (−x, −y) and isirradiated to the position u on the radiation detector. Likewise, a beamirradiated from phase β+3π/2 passes through a voxel (y, −x) andirradiated to the position u on the radiation detector. Thus, byperforming back projection from the grouped data to four pixels whichuse the same radiation detector position data, it is possible tocalculate the radiation detector position and reduce the number of timesinterpolation parameters are calculated.

FIG. 26 shows a case where the amount of calculation in the rowdirection is ½n (where n denotes the number of data revolutions) andrpitch=J/2N (where N is an integer). As shown here, suppose an x-y-zspace (Euclidean space) is considered and a relative moving speedbetween an object and radiation source in the go-around axis direction(e.g., bed feeding speed) is J and a beam passing through a voxel I (x,y, z) irradiated from a focus position S(β) which is phase β isirradiated to the position v in the go-around axis direction on theradiation detector. A beam irradiated from phase β+2π and passingthrough a voxel (x, y, z+J) is irradiated to the position v in thego-around axis direction on the radiation detector as in the case wherethe beam is irradiated from phase β to the voxel I (x, y, z). Likewise,a beam irradiated from phase β+π passes through a voxel I (−X, −y,z+J/2) and is irradiated to the position v in the go-around axisdirection on the radiation detector. Taking advantage of this, theobject is associated with the relative moving speed of the radiationsource in the go-around axis direction according to the reconfigurationintervals and data pieces with phases differing by Nπ (N=1, 2, 3 . . . )[rad] from one another are grouped and back projected group by group.

According to such group-by-group back projection, by associating thepixel intervals of the voxel in the body axis direction at MDCT with theobject and the relative moving speed of the radiation source in thego-around axis direction, it is possible to calculate the position inthe body axis direction at high speed, and when an image is created fromdata of a plurality of revolutions obtained by taking images through aspiral scan, it is possible to enhance the speed of back projectionwhich takes a maximum time to create images.

Here, the spiral period in the body axis direction is synchronized withthe period of the reconfigured voxel in the body axis direction, andwhen, for example, the pixel interval (voxel pitch) in the body axisdirection is rpitch[mm/(unit time)], the relative moving speed (bedmoving speed) of the radiation source in the body axis direction withrespect to the examinee is set to tables=2·N·rpitch (N=1, 2, 3, . . . ).In this way, at the phase of the radiation source which is Nπ (N=1, 2,3, . . . ) [rad], the positions on the radiation detector at which thebeams passing through the voxel I (x, y, z) whose body axis directionposition is Z [mm] and the voxel I (−x, −y, N·J/2+Z) whose body axisdirection position is (N·J/2)+Z [mm] intersect with each other are thesame, and therefore calculating a beam passing through a voxel with aview at the time of back projection is equivalent to simultaneouslycalculating the row positions at phases differing by Nπ (N=1, 2, 3, . .. ) [rad] from each other. Thus, calculations of the row directionpositions of the radiation detector and interpolation coefficients overthe total measuring range are completed within the π [rad] range in theview direction.

In the above described embodiment, no rearrangement in the radiationdetector row direction is performed so that descriptions in therearrangement processing do not become complicated, but to enhance thespeed of back projection, it is also possible to perform rearrangementin the row direction on the plane located at the rotation center whichcrosses the parallel beam at right angles as expressed in P_(para)(β, t,v)=P_(fan)(φ+α, α, (SID/SOD·cos (α))·(v−J·α/2π)) where α=arcsin(t/SOD)as shown in FIG. 13A so that points of intersection in the parallel beamchannel direction become the same v coordinates. When such arearrangement in the row direction is performed, it is possible toreduce the number of arcsin calculations used to calculate α at the timeof back projection and realize faster processing. In this case, theoperating data phase range for each voxel can be likewise calculatedwith H(x, y, φ) in the above described expression changed to Expression33.

$\begin{matrix}{{H\left( {x,y,\phi} \right)} = {\left( {z - \frac{J \cdot \phi}{2\;\pi}} \right) \cdot \frac{{s\_ tz}{\_ dist}\left( {x,y,\phi} \right)}{{{s\_ tz}{\_ dist}\left( {x,y,\phi} \right)} + {w\left( {x,y,\phi} \right)}}}} & \left\lbrack {{Expression}\mspace{14mu} 33} \right\rbrack\end{matrix}$

Furthermore, in this case, v in Expression 22 is changed to v=(z−(J/2π)(φ+α))·SOD cos α/(SOD cos α−x sin φ+y cos φ) to obtain the projectionbeam used for back projection.

Furthermore, the tomograph in the above described embodiment is alsoapplicable to products using X-rays, gamma rays, neutron rays, positron,electromagnetic energy or light. Furthermore, the scan system is notlimited to any of first-generation to fourth-generation systems and thistomograph can also be used for a multi-tube CT incorporating a pluralityof radiation sources and doughnut type tube CT. Furthermore, with regardto the shape of the radiation detector, this tomograph is alsoapplicable to any radiation detector such as detectors arranged on acylindrical surface centered on the radiation source, plane detectors,detectors arranged on a spherical surface centered on the radiationsource and detectors arranged on a cylindrical surface centered on ago-around axis, etc. Furthermore, the position of a radiation detectorcorresponding to the reconfigured voxel is calculated every time, butfor grouping in the channel direction, it is also possible to store atable of reconfiguration parameters calculated beforehand correspondingto N/4 revolutions (0≦β<Nπ/2, N=1, 2, 3 . . . ) in a memory, read thisstored parameter table at the time of reconfiguration and realizereconfiguration based on this parameter table. Adopting such aconfiguration allows calculations of addresses corresponding to 4 viewsall at once. Such simplification of calculations is a techniqueunparalleled in conventional examples. The above described N/4revolutions apply to the case where the shape of a display pixel isrectangular and when the display pixel is hexagonal, data can also begrouped every N/6 revolutions.

Embodiment 4

FIG. 27 is a flow chart showing a processing operation ofreconfiguration means 22 in a tomograph according to an embodiment ofthe present invention.

First, the reconfiguration means 22 is provided with operating dataphase range calculation means for determining a projection data phaserange capable of back projection for each reconfigured voxel,approximate straight line calculation means for calculating anapproximate straight line for a curve indicating the radiation sourceposition with respect to the channel direction position corresponding toa region in concern of parallel beam projection data obtained by aparallel beam of a parallel shape viewed from the go-around axisdirection generated from the radiation source, cone angle correctionmeans for multiplying each row of projection data by a coefficient whichis dependent on the angle of inclination of radiation from the radiationsource, one-dimensional rearrangement processing means for obtainingparallel beam projection data from the fan beam projection data obtainedby a fan-shaped fan beam viewed from the go-around axis directiongenerated from the radiation source, filter correction means forsuperimposing a reconfiguration filter on the parallel beam projectiondata and creating filter-processed parallel beam projection data andparallel beam three-dimensional back projection means forthree-dimension back projecting the filter-processed parallel beamprojection data to a back projection region corresponding to a region inconcern along the approximate irradiation trace of the radiation beamcalculated using the approximate straight line based on the determinedprojection data range capable of back projection.

Based on the above described structure, the data range used for eachvoxel is determined using the operating data phase range calculationmeans in step S4 first, and an approximate straight line for a curveindicating the radiation source position with respect to the channeldirection position of the parallel beam projection data obtained by aparallel beam of a parallel shape viewed from the go-around axisdirection generated from the radiation source by the approximatestraight line calculation means is calculated in step S14. Next, in stepS5, the cone angle correction means multiplies each row of theprojection data by a coefficient which is dependent on the angle ofinclination of radiation and in step S6, the one-dimensionalrearrangement processing means associates the fan beam projection dataobtained from a fan-shaped fan beam viewed from the go-around axisdirection generated from the radiation source with the parallel beamprojection data. Then, in step S7, the filter correction meanssuperimposes a reconfiguration filter on the parallel beam projectiondata and creates parallel beam projection data subjected to filterprocessing. Then, in step 15, based on the projection data range capableof back projection determined by the parallel beam three-dimensionalback projection means, the parallel beam projection data subjected tofilter processing is three-dimensional back projected to the backprojection region corresponding to the region in concern along theapproximate irradiation trace of the radiation beam calculated using anapproximate straight line.

Steps S4 to S7 are the same as those already explained in otherembodiments.

The calculation of an approximate straight line by the approximatestraight line calculation means in step S14 for the curve indicating theradiation source position with respect to the channel direction positionof the parallel beam projection data obtained by a parallel beam of aparallel shape viewed from the go-around axis direction generated fromthe radiation source will be explained.

Here, a technique using a least squares method will be shown. First,when an approximated curve and an approximate curve will be considered.A coordinate Z_(i) of the focus at the channel i position of a parallelbeam is expressed by the following Expression 34 and an approximatestraight line z_(A) except an arcsin calculation is expressed by thefollowing Expression 35. Here, suppose the position of the channel i ofthe parallel beam in the t axis direction is t_(i).z _(i) =J·arcsin(t _(i) /SOD)/2/π  [Expression 34]z _(A)(t _(i))=A·t _(i) +B  [Expression 35]

A, B in the expression can be calculated more specifically as follows.

When points on the approximated curve within a diameter FOV of thecircular region in concern shown in FIGS. 28A and 28B are approximatedwith an approximate straight line and an evaluation function forminimizing the error between the approximated curve and approximatestraight line is used according to a least squares method, the pointscan be expressed by Expression 36. N_(t) denotes the number of samples.

$\begin{matrix}{{E^{2}\left( {A,B} \right)} = {{\sum\limits_{i = 1}^{N_{t}}\left( {z_{i} - {z_{A}\left( t_{i} \right)}} \right)^{2}} = {\sum\limits_{i = 1}^{N_{t}}\left( {z_{i} - {A \cdot t_{i}} - B} \right)^{2}}}} & \left\lbrack {{Expression}\mspace{14mu} 36} \right\rbrack\end{matrix}$

Here, Expression 36 is minimized to determine A, B. With the minimumvalues, the differentiation values with respect to A and B of Expression44 are zeros as shown in Expression 37 and Expression 38.

$\begin{matrix}{O = {\frac{\partial E^{2}}{\partial B} = {{- 2}\;{\sum\limits_{i = 1}^{N_{i}}\left( {z_{i} - {A \cdot t_{i}} - B} \right)}}}} & \left\lbrack {{Expression}\mspace{14mu} 37} \right\rbrack \\{O = {\frac{\partial E^{2}}{\partial A} = {{- 2}\;{\sum\limits_{i = 1}^{N_{i}}\left\{ {t_{i} \cdot \left( {z_{i} - {A \cdot t_{i}} - B} \right)} \right\}}}}} & \left\lbrack {{Expression}\mspace{14mu} 38} \right\rbrack\end{matrix}$

For simplicity, when the following sums in Expression 39 are introducedand these sums are substituted into Expression 36 and Expression 37,then Expression 40 and Expression 41 are obtained.

$\begin{matrix}\begin{matrix}\begin{matrix}{{S \equiv {\sum\limits_{i = 1}^{N_{t}}l}},} & {{S_{t} \equiv {\sum\limits_{i = 1}^{N_{t}}t_{i}}},} & {{S_{z} \equiv {\sum\limits_{i = 1}^{N_{t}}z_{i}}},} & {{S_{t\; t} \equiv {\sum\limits_{i = 1}^{N_{t}}t_{i}^{2}}},}\end{matrix} \\{S_{t\; z} \equiv {\sum\limits_{i = 1}^{N_{t}}\left( {t_{i} \cdot z_{i}} \right)}}\end{matrix} & \left\lbrack {{Expression}\mspace{14mu} 39} \right\rbrack\end{matrix}$B·S _(t) +A·S _(t) =S _(z)  [Expression 40]B·S _(t) +A·S _(t·t) =S _(tz)  [Expression 41]

The solution of these simultaneous equations is given in the followingExpression 42 to Expression 44.Δ≡S·S _(tt)−(S _(t))²  [Expression 42]A=(S _(tt) ·Sz−S _(t) ·S _(tz))/Δ  [Expression 43]B=(S·S _(tz) −S _(t) ·S _(z))/Δ  [Expression 44]

Thus, by substituting this into z_(A)(t_(i))=A·t_(i)+B shown inExpression 35, it is possible to obtain Expression 45.z _(A)(t _(i))=((S _(tt) ·S _(z) −S _(t) ·S _(tz))/Δ))·t _(i)+(S·S _(tz)−S _(t) ·S _(z))/Δ  [Expression 45]

Next, based on the determined projection data range capable of backprojection in step S15 shown in FIG. 27, the parallel beamthree-dimensional back projection means which performs three-dimensionalback projection on the parallel beam projection data subjected to filterprocessing to the back projection region corresponding to the region inconcern along the approximate irradiation trace of the radiation beamcalculated using an approximate straight line will be explained.

As shown in FIG. 28A and FIG. 29, suppose the reconfigured voxel is I(x, y, z), the relative movement distance of the radiation source 11with respect to the examinee per rotation of the scanner on theradiation detector is J, the go-around axis direction position on thecylindrical radiation detector 13 centered on the radiation source 11 isv, the position on the T axis substantially perpendicular thereto is tand the coordinates are T(x, y, φ), then Expression 46 to Expression 50are obtained respectively. In FIG. 29, reference character A denotes animage array of I(x, y, z) and 111 denotes an X-ray beam.

Expression 46 shows a weighting three-dimensional back projection alongthe beam trace over the back projection data range determined by thedata phase range calculation means.

Expression 50 shows a radiation beam trace calculated using anapproximate straight line.

$\begin{matrix}{{I\left( {x,y,z} \right)} = {\int_{B_{s}{({x,y,z})}}^{B_{e}{({x,y,z})}}{{{fP}_{para}\left( {\phi,t,v} \right)} \cdot {W\left( {\phi - {B_{s}\left( {x,y,z} \right)} - \frac{f\;\pi}{2}} \right)} \cdot {\mathbb{d}\phi}}}} & \left\lbrack {{Expression}\mspace{14mu} 46} \right\rbrack\end{matrix}$L(x,y,φ)=√{square root over (SOD ² −t ²)}−x·sin φy·cos φ  [Expression47]t(x,y,φ)=x·cos φ+y·sin φ  [Expression 48]v=(z _(I) −z _(S))·SID/L(φ,x,y)  [Expression 49]

$\begin{matrix}\begin{matrix}{z_{S} = {\frac{J \cdot \left( {\phi + {\arcsin\left( \frac{t}{SOD} \right)}} \right)}{2\;\pi} + Z_{SO}}} \\{\cong {\frac{J \cdot \phi}{2\;\pi} + {A \cdot t} + B + z_{SO}}}\end{matrix} & \left\lbrack {{Expression}\mspace{14mu} 50} \right\rbrack\end{matrix}$

Here, in the three-dimensional back projection, projection data and areconfigured image which should actually be handled discretely arehandled as continuous data, and therefore it is actually necessary tocalculate the data discretely using a combination of interpolation inthree directions of the phase direction (time direction), radiationdetector row direction and radiation detector channel direction using apublicly known interpolation method such as Lagrange interpolation.

As is evident from the above described reconfiguration method,Expression 50 has a large calculation load with an arcsin calculationincluded in the calculation of the focus z position of the conventionalparallel beam as seen from a comparison with Expression 1, but thisarcsin calculation is replaced by an approximate straight line, andtherefore it is possible to simplify an amount of calculation of theparallel beam three-dimensional back projection method and drasticallyenhance the processing speed.

However, this reconfiguration method may involve the risk ofdeterioration of accuracy due to the use of the approximate straightline, but this error remains at such a level that even when the diameterof FOV of a circular region in concern is 410 [mm], the distance SODbetween the focus and go-around axis is 600 [mm], the distance SIDbetween the focus and detector is 1000 [mm], the number of detector rowsrow is 64 [rows], the detector element direction size dapp is 1 [mm] andthe relative moving speed T is 60 [mm/rot], a maximum error is on theorder of 0.023 [mm] and absolute error average is on the order of 0.014[mm]. This error is an error on the order of 2% (maximum 4%) consideringthe measuring accuracy and the z direction width of the beam at therotation center of 0.6 [mm] and is at a totally insignificant leveltaking into consideration that noise is included in measuring data. Thatis, the approximate calculation will not lead to deterioration of imagequality.

Furthermore, in the process of determining the phase range for eachvoxel shown in step S4, a phase range of fπ [rad] is determined in theview direction and a three-dimensional reconfiguration method wherebyredundancy correction is performed using a weighting function is used,and therefore by providing the data with redundancy (extending the backprojection phase width beyond 180 degrees) and assigning weights using aweighting function, it is possible to reduce discontinuity at the dataends, that is, at the of start and end of image taking and obtain animage with the influence of movement of the examinee suppressed to aminimum.

Furthermore, when a fan beam is rearranged to parallel beams and thenone-slice reconfigured image is reconfigured through three-dimensionalback projection, the conventional art uses the same back projectionphase range for all voxels, and the z direction positions of the focusesof parallel beams are not the same in the channel direction, andtherefore a maximum cone angle back projected at each voxel increases.That the maximum cone angle used increases means that a wider detectoris required depending on the go-around axis z direction, that is, therelative moving speed in the z direction between the examinee and focusdecreases and the measuring throughput deteriorates. However, in thisembodiment, the maximum cone angle of the beam used for back projectionis reduced as described above, and therefore it is possible toreconfigure a detector which is narrow in the z direction and improvethe measuring throughput.

Embodiment 5

FIG. 30 is a flow chart showing a processing operation ofreconfiguration means 22 of a tomograph according to a still furtherembodiment of the present invention.

Here, the reconfiguration means 22 consists of operating data phaserange calculation means for determining projection data phase rangecapable of back projection for each reconfigured voxel, approximatestraight line calculation means for calculating an approximate straightline for a curve indicating the radiation source position with respectto the channel direction position of parallel beam projection dataobtained by a parallel beam of a parallel shape viewed from thego-around axis direction generated from a radiation source, cone anglecorrection means for multiplying each row of projection data by acoefficient which is dependent on the angle of inclination of radiation,one-dimensional rearrangement processing means for associating fan beamprojection data obtained from a fan beam of a fan shape viewed from thego-around axis direction generated from the radiation source with theparallel beam projection data, filter correction means for superimposinga reconfiguration filter on the corrected projection data and creatingfilter-processed projection data, redundancy correction weighting meansfor carrying out a redundancy correction on the filter-processedprojection data over a projection data range fπ determined by theoperating data phase range calculation means using a weighting functionwhose shape changes according to the phase width and parallel beamthree-dimensional back projection means for performing three-dimensionalback projection to a back projection region along an approximateirradiation trace of the radiation beam calculated based on theapproximate straight line obtained by the approximate straight linecalculation means while carrying out weighting processing on thefilter-processed projection data using this redundancy correctionweighting means.

As in the case of FIG. 27, such reconfiguration means 22 superimposes areconfiguration filter on the parallel beam projection data using thefilter correction means in step S7, generates filter-processed parallelbeam projection data and then in step S9, carries out a redundancycorrection on the filter-processed projection data created by the filtercorrection means using a weighting function by the redundancy correctionweighting means over the data range fπ determined by the operating dataphase range calculation means. Then, while performing weightingprocessing using this redundancy correction weighting means, in step 15,the filter-processed parallel beam projection data is three-dimensionback projected to a back projection region corresponding to a region inconcern along an approximate irradiation trace of the radiation beamcalculated using an approximate straight line based on the projectiondata range capable of back projection determined by the parallel beamthree-dimensional back projection means.

Details of each step have already been explained with the same stepnumbers assigned, and therefore explanations thereof will be omitted.

The embodiment explained using the above described flow chart in FIG. 27has described the calculation of a data range whose maximum cone angleis narrow in the determining process of the operating data phase rangeby the operating data phase range determining means, but it is alsopossible to determine a data range for each voxel so that in step S4,the difference in the cone angle (corresponding to the absolute value ofv) at the ends (data start/end positions) of the back projection datarange becomes a minimum and perform a similar reconfiguration processbased on this determined data range.

An example of the method of determining the operating data phase rangefor each voxel (calculation of a data range whose back projection phasewidth is narrow) will be explained. First, the case where the zdirection size (Z_(det)) of the radiation detector is sufficiently widewill be shown. When data can be acquired in the same go-around phaserange at all reconfigured voxels at the same z position (whenreconfiguration is possible), or more specifically, when the imagetaking condition in Expression 51 is satisfied, the phase range having asmall difference in the back projection phase range with respect to avoxel whose z position is located within the same plane is expressed byExpression 52, where θ0 is the phase at which the z position of thefocus corresponds to the voxel position, dapp is the z direction size ofthe detector element and row is the number of detector rows.

$\begin{matrix}{J \leqq \frac{{dapp} \cdot \left( {{row} - 1} \right) \cdot \left( {{SOD} - {{FOV}/2}} \right)}{\frac{SID}{2\;\pi}\left( {{f\;\pi} + {2{\arcsin\left( \frac{FOV}{2{SOD}} \right)}}} \right)}} & \left\lbrack {{Expression}\mspace{14mu} 51} \right\rbrack\end{matrix}$θ₀ −fπ/2≦θ<θ₀ +fπ/2  [Expression 52]

However, when the relative moving speed between the examinee and thefocus is high and it is impossible to acquire data at all voxels withinthe same phase range, that is, when the above described image takingcondition is not satisfied, it is not possible to select the phase rangeas expressed in Expression 52. In such as case, it is possible todetermine the phase range using the method shown below.

If the distance between the radiation source and the rotation center isSOD, the relative movement distance of the radiation source relative tothe examinee per rotation of the scanner on the radiation detector is J,the go-around phase of the fan beam source is β, the beam spreadingangle between the beam directed to the reconfigured voxel and centralbeam is α and the go-around phase of the parallel beam is φ, then theradiation source position S(β)=S(x_(s), y_(s), z_(s)) is expressed byExpression 2 described above.

In terms of parallel beams obtained through a rearrangement process,this is expressed by Expression 12 described above.

Here, if the traveling direction of the parallel beam is w and thedirection perpendicular to this w is t, then the t coordinate and wcoordinate when the parallel beam with phase φ passes through thecoordinates (x, y) are expressed by Expression 13 and Expression 14described above and the distance between the radiation source and tzplane (plane passing through the go-around axis and perpendicular to theparallel beam) is expressed by Expression 6 described above.Furthermore, when the parallel beam with phase φ passes through thereconfigured voxel (x, y, z) and crosses the detector whose distancefrom the radiation source is SID and the coordinates of the detector inthe v axis (go-around axis) direction are H(x, y, φ), then this can beexpressed by Expression 7 described above.

Furthermore, if a phase range index is f, in order to back project thereconfigured voxel I (x, y, z) within a phase range having a smalldifference in the back projection phase range with respect to the voxelwhose z position is located within the same plane, the z directionposition of the radiation detector when the beams irradiated from theend positions B_(s) and B_(e) of the phase range fπ used pass throughthe reconfigured voxel and cross the radiation detector must be locatedwithin the range of the detector, and therefore if the go-around phasewhen the z direction position of the focus is at the position of thereconfigured voxel is θ₀, it is possible to select such φ that satisfiesExpression 53 and Expression 54 and approximates to θ₀−fπ/2 infinitely.H(x,y,φ)≦dapp·(row−1)/2  [Expression 53]H(x,y,f+fπ)≧−dapp(row−1)/2  [Expression 54]

More specifically, when θ₀=0, as in step S20 shown in FIG. 31, if theinitial value of φ is −fπ/2 and the phase accuracy to be calculated is Q(e.g., Q is a phase angle by which the focus advances per one view), ifφ is small (φ<0), H (x, y, φ) decreases as φ increases and H(x, y, φ)increases as φ decreases, and therefore if images are taken underreconfigurable conditions, the processes shown in Expression 55 andExpression 56 are repeated until Expression 61 and Expression 62 aresatisfied respectively as shown in steps S21 to S24. This makes itpossible to satisfy Expression 57 and Expression 58 and select φ so asto approximate to θ₀−fπ/2 as much as possible. In this way, the phaserange (Bs≦φ<Be) becomes the same as that expressed by Expression 12 andExpression 13.if [dapp·(row−1)/2−H(x,y,φ)<0],φ=φ+Q  [Expression 55]if [dapp(row−1)/2+H(x,y,φfπ)<0],φ=φ−Q  [Expression 56]H(x,y,φ)≦dapp(row−1)/2  [Expression 57]H(x,y,fπ)≧−dapp·(row−1)/2  [Expression 58]

In this phase range calculation process, by determining the backprojection phase range for each voxel so that the number of views isreduced, it is possible to improve time resolution for each voxel andobtain good image quality in regions where the examinee movesdrastically by combining this with the aforementioned weighting backprojection. Furthermore, by setting the back projection phase range foreach voxel to within a time range in which images are taken at the sametime wherever possible so that the time positions of the respectivevoxels in the displayed images come closer to one another, it ispossible to shorten the time width contributing to the reconfiguredimage and improve time resolution. The back projection phase range inthis case is ideally the same back projection phase range at all voxels,but even when the relative moving speed between the examinee and focusis high and it is impossible to obtain data at all voxels within thesame phase range, it is possible to determine the back projection phaserange for each voxel so that the examinee and focus come as close aspossible to each other.

To arbitrarily make changeable the relationship between a noise leveland body axis resolution in the reconfigured image, a body axis(go-around axis) direction filter whose spatial frequency characteristicis changeable in the row direction is preferably superimposed on theprojection data. This superimposition of the body axis direction filter(body axis direction filtering) may be performed before or after theone-dimensional rearrangement process. The superimposition may also beincluded in the filter correction processing. Furthermore, the abovedescribed embodiment uses a tomograph using X-rays, but the presentinvention is not limited to such a tomograph and is also applicable to atomograph using neutron rays, positron, gamma rays or light.Furthermore, the scan system is not limited to any one of thefirst-generation, second-generation, third-generation orfourth-generation systems, but can also be used for a multi-tube CTprovided with a plurality of radiation sources, cathode scan CT orelectron beam CT. Furthermore, the shape of the radiation detector isalso applicable to any one of radiation detectors such as radiationdetectors arranged on a cylindrical surface centered on a radiationsource, plane detectors, radiation detectors arranged on a sphericalsurface centered on the radiation source, radiation detectors arrangedon a cylindrical surface centered on the go-around axis, etc.Furthermore, the tomograph is not limited to a spiral orbit scan, but isalso applicable to a circular orbit scan. Furthermore, projection dataand reconfigured image that should actually be handled discretely arehandled as continuous data, and therefore it is desirable to calculatediscretely through interpolation in three directions of phase direction,row direction and channel direction of the radiation detector using aninterpolation method such as Lagrange interpolation. Furthermore, theabove described embodiment approximates arcsin with one approximatestraight line, but it is also possible to approximate arcsin using aplurality of approximate straight lines (using different approximatestraight lines according to the distance from the go-around axis).Furthermore, a nonlinear function value of the present invention canalso be calculated using advance calculations (tabulation) andinterpolation for speed enhancement.

In the above described embodiments, the process (S4) of determining thephase range of the projection data used for each voxel in FIG. 9 is alsoapplicable to other embodiments of the reconfiguration means 22.

The redundancy correction weighting process (S9) in FIG. 16 is alsoapplicable to other embodiments of the reconfiguration means 22.

The process (S11) of rearrangement into data with a view of a multipleof 4 and process (S12) of grouping in FIG. 23 are also applicable toother embodiments of the reconfiguration means 22.

The process (S13) of rearrangement in FIG. 24 is also applicable toother embodiments of the reconfiguration means 22.

The approximate straight line calculation process (S14) and parallelbeam three-dimensional back projection process (S15) in FIG. 27 are alsoapplicable to other embodiments of the reconfiguration means 22.

As described above, according to the tomograph of the present invention,when reconfiguration is performed from data obtained through a scan, itis possible to reduce the distortion due to data discontinuity to aminimum and obtain images of high quality without producing any streakartifact in the reconfigured image.

Furthermore, according to the tomograph of the present invention, it ispossible to simplify an arcsin calculation used so far, enhance thespeed drastically and obtain images of high quality in a short time bycalculating an approximate straight line for a curve indicating theradiation source position with respect to the channel direction positionof parallel beam projection data obtained by a parallel beam of aparallel shape viewed from the go-around axis direction generated fromthe radiation source.

All the foregoing descriptions have been presented about theembodiments, but it is obvious for those skilled in the art that thepresent invention is not limited to these embodiments but can be alteredor modified in various ways without departing from the spirit andaccompanying claims.

This application with claims of priority is based on Japanese PatentApplication No. 2002-304463 and Japanese Patent Application No.2003-078125, entire content of which is expressly incorporated byreference herein.

1. An X-ray tomograph comprising: a radiation source and a radiationdetector arranged opposite to each other, between which a bed with anexaminee placed thereon is provided, said radiation source and radiationdetector turning around said bed which is configured to move withrespect to a go-around axis, radiation irradiated from said radiationsource and passing through the examinee being detected using saidradiation detector and being converted to projection data; andreconfiguration means for creating a three-dimensional tomographic imagein a region in concern of the examinee from the projection data, whereinsaid reconfiguration means determines, for each voxel, a projection dataphase range as an angle between 180 and 360 degrees from projection dataobtained at a spiral orbit scan so that a difference in absolute valuesof cone angles at both ends of the projection data phase range used isminimized, superimposes a reconfiguration filter, assigns weights todata of a same phase or opposite phase for each phase for the projectiondata phase range1 and three-dimension back projects the filter-processedprojection data over said projection data phase range determined foreach voxel along an irradiation trace of a radiation beam.
 2. The X-raytomograph according to claim 1, wherein the projection data phase rangeused is determined so as to be the same phase range for each voxel. 3.The X-ray tomograph according to any one of claims 1 and 2, whereinprojection data for a number of images taken per rotation that is amultiple of a number of sides C of a rectangle or hexagon is acquired,and said reconfiguration means comprises back projection means forsuperimposing said reconfiguration filter on the acquired projectiondata, grouping data at a same channel position and having projectionphases in a go-around direction shifting by 2 Nπ/C (N=1, 2, 3, . . . )radians at a time and performing back projection to a square image arraygroup by group.
 4. The X-ray tomograph according to any one of claims 1and 2, wherein said reconfiguration means converts the projection dataobtained to data including fan beam data and parallel beam data for anumber of images taken per rotation that is a multiple of a number ofsides C of a rectangle or hexagon, superimposes the reconfigurationfilter on the converted data, groups data at a same channel position andhaving projection phases in a go-around direction shifting by 2Nπ/C(N=1, 2, 3, . . . ) radians at a time and performs back projection to asquare image array group by group.
 5. The X-ray tomograph according toclaim 1, further comprising associating means for associating voxelpitch in a body axis direction with a relative moving speed between theexaminee and said radiation source in a go-around axis direction.
 6. TheX-ray tomograph according to claim 5, wherein said associating means isconstructed so that a relationship between voxel pitch rpitch in thebody axis direction of a square image and the relative moving speed inthe go-around axis direction of the examinee and said radiation sourceis expressed by 2·N·rpitch (N=1, 2, 3 . . . ).
 7. The X-ray tomographaccording to claim 6, wherein at the phase of Nπ (N=1, 2, 3, . . . )radians of the radiation source, the position on the radiation detectorat which the beam passing through a voxel I (x, y, Z) whose body axisdirection position is Z millimeters intersects and the position on theradiation detector at which the beam passing through a voxel I (−x, −y,NJ/2+Z) whose body axis direction position is N·J/2+Z millimetersintersects are the same.